Finding the Meshgrid provided a surface.

2019 1 8
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更新时间：2019 1 9
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Hi All, given a surface, is there anyway to find the underlying meshgrid of the surface. For example, I have a surface given by function Z that has been created in the following manner:
x = -4:0.4:4; y = -8:0.4:8; [X,Y] = meshgrid(x,y);
Z = comp_z(X,Y);
%Given just the surface, Z , is there a way to find the meshgrid that created it?

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Stephen23
Stephen23 2019-1-9
编辑：Stephen23 2019-1-9
"Given just the surface, Z , is there a way to find the meshgrid that created it?"
In general this is not possible. Consider a simple 2D example: if I give you:
Y = [0,-0.70711,-1,-0.70711,0,0.70711,1,0.70711,0]
can you tell me which X values I used the generate those Y values?:
Y = sin(X)
Unless you have other information (e.g. about the shape of the curve, sample spacing, a range, a domain and some other restrictions, etc) then the general answer is this is not possible.

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Cris LaPierre
Cris LaPierre 2019-1-8

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How are you given the surface? As a fig file? You could extract the X and Y indices of the surface:
x = -4:0.4:4;
y = -8:0.4:8;
[X,Y] = meshgrid(x,y);
Z = (X.*Y);
surf(X,Y,Z)
h = findobj('Type','Surface');
surfX = h.XData;
surfY = h.YData;
all(all(surfX==X))
ans =
1
all(all(surfY==Y))
ans =
1

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Carlos Pedro
Carlos Pedro 2019-1-8
Hi Cris, thanks for your assistance,
Basically, its part if a bigger function, I want to be able to input a surface,Z ( a function of x and y), into the function and be able to interpolate values of Z (using cubic interpolation) at different points. This is what I have so far:
function [z0] = myinterp_function(Z,x0,y0)
X =?
Y = ?
fun_interp = griddedInterpolant(X',Y',Z','cubic');
z0 = fun_interp(x0,y0);
end
Essentialy I want Z to be defined outside of the function but for this to work I will need a way to get X and Y from Z.
Cris LaPierre
Cris LaPierre 2019-1-8
So it's not a surface in MATLAB yet. You have a matrix of numbers and want to somehow reverse engineer it to get what the values of X and Y were to compute the Z values?
Can you not also pass in your X and Y values?
The only other option I can think of is to use your equation and the z values you have. Create a defined interpolated grid of x values and solve for the corresponding y values.
Carlos Pedro
Carlos Pedro 2019-1-8
Yes exactly, I just want to pass Z in and retrieve X and Y inside the function so I can perform the interpolation.
No I need to define Z outside of the function.
The Z function I have is: z = cos(x/2).* cos(y) + (y/10) - (x/5);
Cris LaPierre
Cris LaPierre 2019-1-8
I didn't say define Z inside the function. I said use the values of Z and your interpolated X to solve for Y. You might be able to use the solve function in MATLAB
Carlos Pedro
Carlos Pedro 2019-1-9
I've had a look and a think and I don't think what I want is possible.
Thankyou regardless.

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